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Full text of "Treatise On Analysis Vol-Ii"

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NOTATION       xiii

space of real-valued locally ^-integrable
functions: 13.13

space   of   complex-valued   locally   IJL-
integrable functions: 13.13
space of classes of real (complex) valued
locally /i-integrable functions: 13.13
integral   with   respect   to   a   complex
measure: 13.16
support of a measure: 13.19
\\H\\                                                   norm of a measure: 13.20

space of bounded real (complex) meas-
ures: 13.20

space   of real  (complex)  valued  con-
tinuous functions which' tend to 0 at
infinity: 13.20
i d/j,,

integral  with  respect  to  the  product
measure A  ju: 13.21
product measure: 13.21

upper integral with respect to a product
measure: 13.21

lower integral with respect to a product

measure: 13.21

the function (x, y)*~+f(x)g(y): 13.21

product of n measures: 13.21

integral with respect to the product of the
n measures: 13.21

\in                                            product   of   an   infinite   sequence   of

measures: 13.21, Problem 9

f, $(s)f                                     translates of a function: 14.1

u, 8(^)ju                                     translates of a measure: 14.1

transforms of a function or measure under
l: 14.1(X, fi)9 LfOu), Lg                        space of classes of pth power integrable